Matrices & determinants worksheet with answers

Free printable Matrices & determinants worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
A =4−738

Find the determinant det A of the matrix A shown.

A = [4 −7; 3 8]
det A =
2.Easy
A =8−72−7

Find the determinant det A of the matrix A shown.

A = [8 −7; 2 −7]
det A =
3.Medium
A =−31−2244−2−3−1

Find the determinant det A of the 3×3 matrix A shown.

A = [−3 1 −2; 2 4 4; −2 −3 −1]
det A =
4.Medium
A =3−51−2B =−4−233

Let C = AB for the matrices shown. Find the entry c11 (row 1, column 1).

A = [3 −5; 1 −2]B = [−4 −2; 3 3]
c11 =
5.Hard
A =6−5−4−3b =1−7

Solve the system 6x − 5y = 1 and −4x − 3y = −7. Find x.

6x − 5y = 1−4x − 3y = −7
x =
6.Hard
A =5312b =−911

Solve the system 5x + 3y = −9 and x + 2y = 11. Find x.

5x + 3y = −9x + 2y = 11
x =

Answer key

  1. 1. det A = 53
  2. 2. det A = −42
  3. 3. det A = −34
  4. 4. c11 = −27
  5. 5. x = 1
  6. 6. x = −7.286

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